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Ordered representations of spaces of integrable functions

Ordered representations of spaces of integrable functions Let X be a Banach space, (Ω,Σ) a measurable space and let m : Σ → X be a (countably additive) vector measure. Consider the corresponding space of integrable functions L 1(m). In this paper we analyze the set of (countably additive) vector measures n satisfying that L 1(n) = L 1(m). In order to do this we define a (quasi) order relation on this set to obtain under adequate requirements the simplest representation of the space L 1(m) associated to downward directed subsets of the set of all the representations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Ordered representations of spaces of integrable functions

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References (11)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
DOI
10.1007/s11117-008-2211-1
Publisher site
See Article on Publisher Site

Abstract

Let X be a Banach space, (Ω,Σ) a measurable space and let m : Σ → X be a (countably additive) vector measure. Consider the corresponding space of integrable functions L 1(m). In this paper we analyze the set of (countably additive) vector measures n satisfying that L 1(n) = L 1(m). In order to do this we define a (quasi) order relation on this set to obtain under adequate requirements the simplest representation of the space L 1(m) associated to downward directed subsets of the set of all the representations.

Journal

Positivity – Springer Journals

Published: Sep 1, 2008

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